In order to implement disease-specific interventions in young age groups, policy makers in low-and middle-income countries require timely and accurate estimates of age-and cause-specific child mortality. High quality data is not available in countries where these interventions are most needed, but there is a push to create sample registration systems that collect detailed mortality information. Current methods that estimate mortality from this data employ multistage frameworks without rigorous statistical justification that separately estimate all-cause and cause-specific mortality and are not adaptable enough to capture important features of the data. We propose a flexible Bayesian modeling framework to estimate age-and causespecific child mortality from sample registration data. We provide a theoretical justification for the framework, explore its properties via simulation, and use it to estimate mortality trends using data from the Maternal and Child Health Surveillance System in China.